1. Field of Invention
The present invention relates to receivers for DSSS/CDMA communication systems. More particularly, the present invention relates to receivers including an MMSE linear detector implemented using Griffiths"" algorithm.
2. Description of the Related Art
Code-division multiple access (CDMA) is one of several methods of multiplexing wireless users. In direct sequence spread spectrum CDMA (DSSS/CDMA) communications systems, users are multiplexed by distinct spreading codes rather than by orthogonal frequency bands, as in frequency-division multiple access (FDMA), or by orthogonal time slots, as in time-division multiple access (TDMA). That is, all CDMA users transmit simultaneously over the same frequency spectrum. In a single-user detector, the conventional receiver operates as a matched correlator to detect the signal of interest by correlating the entire received signal with the particular user""s code waveform. Since the received signal is composed of the sum of all users"" signals plus additive white Gaussian noise (AWGN), the signals from other users will deteriorate the performance of the matched correlator. This fact results from the random time offsets between users, which make it impossible to design the code waveforms to be completely orthogonal. Multiple access interference (MAI) is thus a factor which limits the capacity and performance of the DSSS/CDMA systems.
The performance of the matched correlator is further degraded by imperfect power control. A nearby interfering user of large power will have a significant impact on the reception of a highly attenuated signal of interest. The so-called near-far problem can be mitigated by an optimal multiuser detector. The detector yields the most likely transmitted sequence of all users to maximize the probability that the estimated sequence was transmitted given the received signal extending over the whole message. This probability is referred to as the joint a posteriori probability, and the receiver is known as a maximum-likelihood sequence (MLS) detector. A problem of the MLS approach is that the implementation complexity is very high. Another disadvantage is that it requires knowledge of the received amplitudes and phases of all users. These values, however, are not known in advance and must be estimated. Therefore, suboptimal but near-far resistant receivers have been developed.
One suboptimal but near-far resistant receiver is a minimum mean-squared error,(MMSE) detector. The MMSE linear detector utilizes the cyclostationarity of the highly structured MAI to mitigate the near-far problem and has a moderate complexity in comparison with the matched correlator. For a particular user, the MMSE detector adopts a finite-impulse response (FIR) filter to estimate the transmitted signal. To mitigate the interference, the FIR filter is designed such that the mean-squared error between the transmitted signal and the estimate is minimized.
A DSSS/CDMA communication system including an MMSE linear detector is disclosed in xe2x80x9cMMSE Interference Suppression for Direct-Sequence Spread-Spectrum CDMAxe2x80x9d by U. Madhow et al., IEEE Trans. Commun., vol. 42, pp. 3178-3188, December 1994, which is incorporated herein by reference. In a system such as disclosed therein, the received signal vector r(j) of one symbol interval can be expressed by                               r          ⁡                      (            j            )                          =                                            ∑                              l                =                1                            L                        ⁢                                                            b                  l                                ⁡                                  [                  j                  ]                                            ⁢                              xe2x80x83                            ⁢                              A                l                            ⁢                              c                l                                              +                      x            ⁡                          (              j              )                                                          (        1        )            
where bl[j]xcex5[xe2x88x921, +1] is the transmitted symbol, Al is the received amplitude, clxcex5RNxc3x971 is the signal srector of the lth user, L is the number of users and x(j) is the vector of AWGN samples. Taking the first user to be the desired transmission, the MMSE linear detector demodulates the symbol of interest as {circumflex over (b)}l[j]=sgn(wTr(j)) where the FIR filter tap-weight vector w minimizes the mean-squared error (MSE) between the desired symbol and the test statistic. The symbol xe2x80x9cTxe2x80x9d indicates the matrix transpose operation. The optimum tap-weight vector wn can be expressed as
wo=Rxe2x88x921pxe2x80x83xe2x80x83(2)
where R=E{r(j)rT(j)} and p=E{bl[j]r(j)} are the correlation matrix of the received signal vector and the cross-correlation vector between the desired signal and the received signal vector, respectively.
The tap-weights of the MMSE linear detector can be obtained by solving the Wiener-Hopf equation. However, the computation load is high since the calculation involves matrix inversion and multiplication. The MMSE linear detector can also be implemented by adaptive algorithms rather than from a direct solution involving matrix computation. The least mean square (LMS) algorithm and the recursive least squares algorithm have been used to train the MMSE detector on the assumption that a pilot signal is available. For practical applications, when ttie interference is time-varying or unknown, the MMSE linear detector can be implemented adaptively by the blind Griffiths"" algorithm. The Griffiths"" algorithm uses the desired signal vector instead of a training sequence of symbols for initial adaptation. When the desired signal vector is perfectly known and the step-size is small enough, the Griffiths"" algorithm will drive the linear detector to converge to the Wiener-Hopf solution. xe2x80x9cBlind Adaptation Algorithms for Direct-Sequence Spread-Spectrum CDMA Single-User Detectionxe2x80x9d by N. Zecevic et al., Proceedings of IEEE Vehicular Technology Conference, pp. 2133-2137, 1991. discloses an adaptive receiver for a DSSS/CDMA system using the Griffiths"" algorithm as the adaptation algorithm, and is incorporated herein by reference.
The Griffiths"" algorithm, like the LMS algorithm, is an approximate implementation of the method of steepest descent. Generally, the method of steepest descent solves the Wiener-Hopf equation by updating the filter tap-weights recursively. Since the method of steepest descent still requires the correlation matrix, the computation load is not easy to handle. Using the instantaneous estimate instead of the correlation matrix can reduce the computation load. The resultant algorithm is the Griffiths"" algorithm.
More particularly, if the correlation matrix R and the cross-correlation vector p are known, the method of steepest descent has an updating equation for a tap-weight vector w expressed as
w(j+1)=w(j)+xcexc[pxe2x88x92Rw(j)]xe2x80x83xe2x80x83(3)
where xcexc is a small fixed step-size. The Griffiths"" algorithm simplifies the updating equation (3) by replacing the correlation matrix with an instantaneous estimate r(j)rT(j), but still must have the knowledge of the cross-correlation vector p in advance. For the DSSS/CDMA communication system, the cross-correlation vector p becomes Alcl, where c1 is the spreading sequence of interest if the timing synchronization between the receiver and the symbol clock of interest is perfect. The Griffiths"" algorithm can thus be expressed as
w(j+1)=w(j)+xcexc[clxe2x88x92z(j)r(j)]xe2x80x83xe2x80x83(4)
where xcexc is a small step-size and z(j)=wT(j)r(j) is the output of the detector.
A disadvantage of the Griffiths"" algorithm is that, like the LMS algorithm, its convergence properties depend on the eigenvalue spread of the correlation matrix associated with the received signal vectors. As the interference level or the number of users increases, the problem of eigenvalue spread will be severe such that the convergence speed of the Griffiths"" algorithm with be very slow.
Several variable step-size (VSS) LMS algorithms have been proposed to accelerate convergence speed. In general, these methods employ a procedure that uses a larger step-size to obtain a faster convergence speed when the error signal is large, and adopt a smaller step-size to obtain a smaller mean-square error as the error signal decreases. For example, xe2x80x9cA Variable Step Size LMS Algorithmxe2x80x9d by R. H. Kwong et al., IEEE Trans. Signal Processing, vol. 40, pp. 1633-1642, July 1992, discloses an LMS algorithm in which the step-size at the jth iteration can be controlled by the instantaneous error signal e(j).
xe2x80x9cA Robust Variable Step Size LMS-Type Algorithm: Analysis and Simulation,xe2x80x9d by T. Aboulnasr et al., IEEE Trans. Signal Processing, vol. 45, pp. 631-639, March 1997, discloses an LMS algorithm which employs an estimate of the correlation between successive error samples e(j) and e(jxe2x88x921) to control the step-size. The controlling algorithm results from the fact that both the error energy and the correlation between successive error samples are small when the LMS filter is converging to the optimum solution.
xe2x80x9cA stochastic gradient adaptive filter with gradient adaptive step size,xe2x80x9d by V. J. Mathews et al., IEEE Trans. Signal Processing, vol. 41, pp. 2075-2087, June 1993, discloses an adaptive filter that controls the step-size according to a stochastic gradient descent procedure on the squared output error.
Generally, numerical simulation results show that the VSS LMS algorithms improve the convergence properties significantly compared to the LMS algorithm with a fixed step-size. However, these VSS LMS algorithms cannot be used for blind training since they require a training sequence.
To achieve these and other advantages and in accordance with the purpose of the invention, as embodied and broadly described, the invention is directed to a receiver for receiving a signal in a direct sequence spread spectrum CDMA (DSSS/CDMA) communication system, in which the received signal is sampled, and in which a weight vector is computed using Griffiths"" algorithm. The receiver comprises means for multiplying the received signal samples with components of a predetermined spreading sequence to provide first products and for summing the first products to provide a first output; means for multiplying the received signal samples with components of the weight vector to provide second products and for summing the second products to provide a second output; and means, coupled to receive the first and second outputs, for computing a step-size for each successive iteration of the Griffiths"" algorithm.
Also in accordance with the present invention there is provided a receiver for receiving a signal in a direct sequence spread spectrum CDMA (DSSS/CDMA) communication system. The receiver comprises means for sampling the received signal; first means for multiplying the received signal samples with components of a predetermined spreading sequence to provide first products and for summing the first products to provide a first output; second means for multiplying the received signal samples with components of a weight vector to provide second products and for summing the second products to provide a second output; means for computing the weight vector using Griffiths"" algorithm, wherein successive iterations of the Griffiths"" algorithm are controlled by a step-size; and means, coupled to receive the first and second outputs, for computing the step-size for each successive iteration of the Griffiths"" algorithm performed by the computing means.
Further in accordance with the present invention there is provided a method for receiving a signal in a direct sequence spread spectrum CDMA (DSSS/CDMA) communication system. The method comprises sampling the received signal and for storing the received signal samples; multiplying the received signal samples with components of a predetermined spreading sequence to provide first products and summing the first products to provide a first output; multiplying the received signal samples with components of a weight vector to provide second products and summing the second products to provide a second output; computing the weight vector using Griffiths"" algorithm, wherein successive iterations of the Griffiths"" algorithm are controlled by a step-size; and computing, based on the first and second outputs, the step-size for each successive iteration of the Griffiths"" algorithm performed by the computing means.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed.
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate an embodiment of the invention and together with the description serve to explain the principles of the invention.